I want to plot the equation that show in the first image by code
the plot is given in a book.

Is easy plot interactive in first order derivate equations, like lorentz atractor, by increase just a bit and evaluate, but have not idea what methods follow to do the plot in this case
UPDATE
If the equation was dϕ/ds+sin ϕ= 0 I plot doing the follow:
Define a constant ds=0.01
Init s, ϕ to some value
Repeat for n interactions :
dϕ=- ds*sin dϕ
ϕ= ϕ+dϕ
s=s+ds
plot(s, ϕ)
the image belows show my code for plot Lorenz´s atractor in Blender with python
